Welcome back @Katie Andrews. You have some good questions.
1) I manage my own properties. IMO, if you are buying a handful of high quality properties, it will be pretty easy to learn the basics of PM that you need to know to make managing a small portfolio a breeze. There is a level of peace of mind that comes with knowing who you give possession of your properties to, that I personally put a high value on. I'm not trying to twist your arm or anything, but high quality properties are not the PM headache that a lot of people cry about.
2) Generally, I would say somewhere in a range of 10-20% of your investment capital should be held as a cash reserve. That is a matter of your risk tolerance and is a good question to ask your lender if you use leverage. If you have other retirement income, I would be real conservative and use a minimal amount of debt if any.
3) The number of properties you buy will depend on what city you are in and whether or not you use leverage? For example, you may want to create $4,000/month of income with your nest egg? How many properties would it take to create that much income? I lean toward "less is more."
4) I recommend you look into note investing. There is a different level of liability risk involved in note investing vs ownership of properties. There's no PM involved in note investing either. We have an over-employment problem here in this state. When you see that about 70-80% of the billboards are plastered with people pushing people to sue somebody, you'll know what I mean by that. Asset protection becomes a major concern if you own a bunch of free and clear properties here.
You sound like you've recently dealt with some estate matters, but the question of your heirs and their ownership interest in any of your assets come to mind as a concern. This works differently most places from here, because we have forced heirship.
Another concern is what will be the tax consequences of the sale of your condo? What portion of the $500k is capital gain (or exempt from gains if this was your personal residence)? How much is subject to recapture rates of tax because you depreciated over the years? Should you do a 1031 Tax Deferred Exchange to be able to reinvest all of your gain? There are rules about reinvesting your gains that will be factors in how much cash you can keep without reinvesting it, if you do the exchange?
Last, I'll say, be careful. A person with cash to invest doesn't have anybody to save them from themselves! I've seen and heard of a lot of mistakes cash buyers made that bank underwriters would have prevented.